When operating the system described in Problem 11.46, the operator decides to suddenly close the valve once steady-state flow has been reached. Assuming that the gasoline is slightly compressible and the piping is elastic, determine:

(a) The acoustic wave speed.

(b) The pressure rise at the valve once the valve is rapidly closed in a manner to cause water hammer.

(c) If the maximum allowable pressure in the pipe is 250 kPa, what can you conclude about the outcome of the water (gasoline) hammer activity? The pipe is made of aluminum, E = 70 GPa, with 2.5-mm-thick walls, and the bulk modulus of elasticity of gasoline is B = 1.05 GPa.

Problem 11.46

Gasoline is supplied by gravity without pumping from a storage tank through a 800-m-long 50-mmdiameter nearly horizontal pipe into a tanker truck. There is a quick-acting valve at the end of the pipe. The difference in elevations of gasoline between the reservoir and the truck tank is 8 m. Initially, the valve is partially closed so that K = 275. Then the operator decides to increase the discharge by opening the valve quickly to the position where K = 5. Assuming an incompressible fluid and an inelastic piping system, determine the new steady-state discharge and the time it takes to reach 95% of that value. Assume that f = 0.015.